The problem asks to factor the quadratic polynomial $21x^2 + 11x - 2$.

1. Problem Description

The problem asks to factor the quadratic polynomial $21x^2 + 11x - 2$.

2. Solution Steps

To factor the quadratic polynomial $21x^2 + 11x - 2$, we look for two numbers whose product is $21(-2) = -42$ and whose sum is $11$. The two numbers are $14$ and $-3$. We can rewrite the middle term using these numbers:

$21x^2 + 11x - 2 = 21x^2 + 14x - 3x - 2$

Now we factor by grouping:

$21x^2 + 14x - 3x - 2 = 7x(3x + 2) - 1(3x + 2)$

Now we factor out the common term $(3x + 2)$:

$7x(3x + 2) - 1(3x + 2) = (7x - 1)(3x + 2)$

3. Final Answer

$(7x - 1)(3x + 2)$